Question

A rock climber climbs 90 feet of steep rock face in the first half–hour of climbing. In each succeeding half–hour, the climber achieves only 80% of the height achieved in the previous half–hour. Find the total height climbed.

Answer 1

The total height climbed is 450 feet if a rock climber climbs 90 feet of the steep rock face in the first half-hour of climbing. In each succeeding half-hour, the climber achieves only 80% of the height achieved in the previous half-hour

What is a sequence?

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

We have:

A rock climber climbs 90 feet of the steep rock face in the first half-hour of climbing.

In the second half rock climber climbed  = 80% of 90 = 72 ft

In the third half hour = 80% of 72 = 57.6 ft

In the fourth half = 80% of 57.6 = 46.08 ft

We have a geometric progression:

90, 72, 57.6, 46.08.... infinitely

Here the common ratio r = 72/90 = 0.8

The sum of the infinite series of a GP = a/(1-r)

= 90/(1-0.8)

= 450 feet

Thus, the total height climbed is 450 feet if a rock climber climbs 90 feet of the steep rock face in the first half-hour of climbing. In each succeeding half-hour, the climber achieves only 80% of the height achieved in the previous half-hour

Learn more about the sequence here:

brainly.com/question/21961097

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